Trig help (1 Viewer)

[cookiez69]

Hey guys,

Could you explain how to work this out?




Thank you

 

[Menomaths]

Hey guys,

Could you explain how to work this out?




Thank you

Exact same question was in my math test LOL
Where did you get this question from?

 

[cookiez69]

It was from a maths in focus text book.

 

[Menomaths]

2tanx = 1
tanx = 1/2
x= 26'34
x= 26'34 and 206'34'
Is that the answer?

 

[cookiez69]

Ah nope sorry, its tan2x = 1 not 2tanx = 1.

The answers are 22.5, 112.5, -67.5 and -157.5 degrees.

 

[yupmynameisnick]

tan2x=1

tan45=1

x=22'30',-157'30',67'30',112'30'

Is this right?

 

[cookiez69]

tan2x=1

tan45=1

x=22'30',-157'30',67'30',112'30'

Is this right?

It's -67'30', I just worked it out myself and got the right answer, but now I'm trying to explain to myself why it works :\

 

[Menomaths]

Ah nope sorry, its tan2x = 1 not 2tanx = 1.

The answers are 22.5, 112.5, -67.5 and -157.5 degrees.

Oh, that's double angle formula I think, something we don't learn in 2U ahah my bad.

 

[yupmynameisnick]

yup -67'30'

I think its because u have to do the opposite when going in a negative direction on the unit circle which is bloody confusing.

 

[Menomaths]

It's -67'30', I just worked it out myself and got the right answer, but now I'm trying to explain to myself why it works :\

Atleast I can help you on this one;
It's negative because you have -pi. You solve the for the pi normally then for -pi the ASTC circle becomes reverse. so its (A)360-theta (S)180+theta (T)180-theta (C)theta
Hope this makes sense.

 

[bedpotato]

It's -67'30', I just worked it out myself and got the right answer, but now I'm trying to explain to myself why it works :\

Whenever there's a number infront of the x, e.g. tan(2x), there's more than one revolution. In this case, there's 2 revolutions. At the end, you divide the answer by 2.
So you would've gotten:
2x = 45', 225, -135' and -315'
But since you're solving for x, you divide everything by 2.
Hope that makes sense..?

 

[cookiez69]

Whenever there's a number infront of the x, e.g. tan(2x), there's more than one revolution. In this case, there's 2 revolutions. At the end, you divide the answer by 2.
So you would've gotten:
2x = 45', 225, -135' and -315'
But since you're solving for x, you divide everything by 2.
Hope that makes sense..?

Yes I already knew that, but my main problem here is, since you do a second revolution don't you add say,
45 + 360 = 405

In my first revolution I get 2x = 45 and -135. In my second revolution I get (45+360=405) and (-135+360=225)

 

[bedpotato]

Yes I already knew that, but my main problem here is, since you do a second revolution don't you add say,
45 + 360 = 405

In my first revolution I get 2x = 45 and -135. In my second revolution I get (45+360=405) and (-135+360=225)

But when you divide 405 by 2 you get 202'30'. But the limit is between -180 and 180. It's right, but just not what the question is asking for. You have to answer the question.

 

[cookiez69]

But when you divide 405 by 2 you get 202'30'. But the limit is between -180 and 180. It's right, but just not what the question is asking for. You have to answer the question.

So how did you get -315' when you add +360 for the second revolution? Sorry for all the questions :\

 

[bedpotato]

Normally you would do 360 - 45, right?
For the second revolution:
360 + 360 is 720.
So basically, 720 - 45 = 675
But since its tan, -675. then just divide by two.

 

[suika]

So how did you get -315' when you add +360 for the second revolution? Sorry for all the questions :\

You don't need to add 360 since the question is asking for an answer between -180 and 180; since 45+360 = 405 > 402/2 = 202'30.

Start from -180, then add 45 since its positive; -180+45 = -135 > -135/2 = -67'30.
Then you can do the same for your second answer however using -360 instead of -180; -360+45 = -315 > -315/2 = 157'30

This is because tan is negative in 2nd and 4th quadrants - therefore using 180-x (2nd quadrant) and 360-x (4th quadrant). Based on the answers above, you are just switching the signs from e.g. 180+45 to -180+45

Tan is positive in the question (hence using x (1st quadrant) and 180+x (3rd quadrant) but it asks for also any negative answers.

I hope that made sense in some way? ^^;

 

[coonsmell]

Normally you would do 360 - 45, right?
For the second revolution:
360 + 360 is 720.
So basically, 720 - 45 = 675
But since its tan, -675. then just divide by two.

No. There's no 360 (well, kinda).

You're starting from the negative 180, not zero. So essentially, you're starting in the Tan quadrant (45 degrees, similar to the All quadrant).

45 degrees for the first one, (180 - 45) for the second quadrant = -135 (Cos quadrant is negative as the equation is Tan), 270-45 = 225 for the next (positive as it's in the ALL quadrant), 360 - 45 = -315 for the last (sine quadrant).

Since it's 2 Theta, you divide these answers by two: 22.5, -67.5, 112.5, -157.5


To help you clarify further, the two doesn't mean two revolutions. It's just a product of the angle. If it was two revs, it would have parameters like 0 < x < 720 which are a bitch.